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Smita04
  A quadrilateral is inscribed in a circle. If the [#permalink]
New postPosted: Thu Feb 02, 2012 6:30 am 
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Kudos (?): 2 (0), given: 31
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A quadrilateral is inscribed in a circle. If the circumference of the circle is 5(pi), what is the area of the quadrilateral?

(1) The length of one of the diagonals of the quadrilateral is 5.
(2) The length of two opposite sides are 3 and 4 respectively.
[Reveal] Spoiler: OA
C


Last edited by Smita04 on Thu Feb 02, 2012 9:44 pm, edited 1 time in total.

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omerrauf
  Re: Geometry [#permalink]
New postPosted: Thu Feb 02, 2012 9:00 am 
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Kudos (?): 32 (0), given: 10
I think the answer should be C. This one is difficult to visualize without drawing. We know the diameter of the circle is 5 and quadrilateral is inscribed

1. Since diagonal is 5, that means the quadrilateral is divided into two triangles with diagonal as the diameter of the circle. Now since they are inscribed. that means the angle both of these form with the Circumference is a right angle. But we do not know the sizes of the sides. Insufficient

2. I can draw various quadrilaterals which are inscribed and have opposite sides as 3 and 4. All of these will have different areas so insufficient.

Now combined I know that one side of one right angled triangle is 3 and of the other right angled triangle is 4 so the remaining two sides will be in the same ratio as well from the pythagorean theorem. Now that we know all 4 sides and the heights (since diagonal is 5 and is the hypotenuse of the right-angled triangle for both triangles that form the quadrilateral. Hence answer should be C.

Whats the OA?

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